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Bionomial theorem/ question (wp)

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data


    For what values of k does the function f(x)= x^3 + 6x^2 +kx -4 give the same remainder when divided by x-1 and x+2?

    answer, however in the booklet it says the answer is 3, why is this? what did i do wrong?

    2. Relevant equations



    3. The attempt at a solution

    So.. i set up two equations one using f(1) and one using f(-2)

    f(1)= 1 + 6 + 1k -4
    f(1) = -2 +k
    2 = k

    f(-2) = 12 -2k
    2k = 12
    k= 6,

    I plugged 6 and 2 into the equation of f(1) and got the same (remainder of 9)

    wat am i doing wrong?
     
  2. jcsd
  3. Sep 27, 2011 #2
    anyone??
     
  4. Sep 27, 2011 #3

    SammyS

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    Patience !!

    Please, wait at least 24 hours before bumping your thread.
     
  5. Sep 27, 2011 #4

    SammyS

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    What does the remainder theorem say?

    Set the two remainders equal to each other. Solve for k.
     
  6. Sep 27, 2011 #5
    wat? like.. 6k = 2?

    6/2 = 3
    k=3?
     
  7. Sep 27, 2011 #6

    eumyang

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    1 + 6 - 4 = -2?

    Where did the f(1) and f(-2) go???? This makes no sense. If you're supposed to get the same remainder when dividing by x - 1 and x + 2, then that means that
    f(1) = f(-2).

    And can you also please double check your work before submitting your post?
     
  8. Sep 27, 2011 #7
    f(1)= 1 + 6 + 1k -4
    f(1) = 7-4+1k
    f(1) = 3+k
    -3=k

    f(-2) = (-2)^3 + 6(-2)^2 + k(-2) -4
    f(-2) = 12 -2k
    2k = 12
    k= 6

    ?? what do i do now
     
  9. Sep 27, 2011 #8

    eumyang

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    Again, why are you making the f(1) disappear? DON'T DO THAT! :mad:

    You say
    f(1) = 3 + k
    and
    f(-2) = 12 - 2k.

    Since the remainders are supposed to be equal,
    f(1) = f(-2)
    so substitute with the right-hand-side of the two previous equations.
     
  10. Sep 27, 2011 #9
    I dont get it... substitute something thats not a full equation into the right hand side of the prev 2 eq? doesnt something have to = k inorder for me to sub it into another equation..?

    How do i substitute dat
     
  11. Sep 27, 2011 #10

    eumyang

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    f(1) = f(-2)
    Instead of f(1), write what it equaled to.
    Instead of f(-2), write what it equaled to.
    That's what I meant by substituting.
     
  12. Sep 27, 2011 #11
    f(1) = 3 + k
    and
    f(-2) = 12 - 2k.


    3+k = 12-2k
    -9 = -3k
    k= 3 ...

    I see, thanks :P
     
  13. Sep 27, 2011 #12

    SammyS

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    That's exactly what I suggested you do back in post #4 .
     
  14. Sep 27, 2011 #13
    gl bk
     
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